Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
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Página 9
... integral, so the symbol used as a summation index does not alter the value of a sum The use of the same index for two summations occurring. 2 miixi = 2 "71ka (1-25) 1' k FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 9.
... integral, so the symbol used as a summation index does not alter the value of a sum The use of the same index for two summations occurring. 2 miixi = 2 "71ka (1-25) 1' k FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 9.
Página 11
... integral value of n. This matrix satisfies the relations Im = ml = m (1.33) It should be noted here that unless m is square, two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its ...
... integral value of n. This matrix satisfies the relations Im = ml = m (1.33) It should be noted here that unless m is square, two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its ...
Página 38
... integral Formula The Cauchy-integral formula states that, if f(Z) has no singularities within or on the contour of integration C and if the point a lies within C, then . f (a) = 1— fi) —f(z) :12 (3.2) 211i 0 Z — a 1 It is assumed that ...
... integral Formula The Cauchy-integral formula states that, if f(Z) has no singularities within or on the contour of integration C and if the point a lies within C, then . f (a) = 1— fi) —f(z) :12 (3.2) 211i 0 Z — a 1 It is assumed that ...
Página 39
... integral is analytic within C. 3.3 Application to Matrices The assertion made in (3.1) will now be discussed. Consider fl)— dZ (3.4) 2111 1 Z — A where C encloses each zero of |Z — Al and no singularity off(Z). It will be shown that ...
... integral is analytic within C. 3.3 Application to Matrices The assertion made in (3.1) will now be discussed. Consider fl)— dZ (3.4) 2111 1 Z — A where C encloses each zero of |Z — Al and no singularity off(Z). It will be shown that ...
Página 40
... integral formula. This procedure is illustrated by the following three examples: (1 ') A = e 1 According to step a in the procedure Z — 1 —~ 1 ' 1““) :() —e Z —— 1 qzl 0 Z — 1 — 0 e><qm>=<> —e z — 1 q,, 1 Example 1 A brief computation ...
... integral formula. This procedure is illustrated by the following three examples: (1 ') A = e 1 According to step a in the procedure Z — 1 —~ 1 ' 1““) :() —e Z —— 1 qzl 0 Z — 1 — 0 e><qm>=<> —e z — 1 q,, 1 Example 1 A brief computation ...
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applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero